1. Field of the Invention
This invention concerns a method for the space-time estimation of one or more transmitters in an antenna network when the wave transmitted by a transmitter is propagated as multipaths.
Multipaths exist when a wave transmitted by a transmitter is propagated along several paths towards a receiver or a goniometry system. Multipaths are due in particular to the presence of obstacles between a transmitter and a receiver.
The field of the invention concerns in particular that of the goniometry of radioelectric sources, the word source designating a transmitter. Goniometry means xe2x80x9cthe estimation of incidencesxe2x80x9d.
It is also that of spatial filtering whose purpose is to synthesise an antenna in the direction of each transmitter from a network of antennas.
2. Discussion of the Background
The purpose of a traditional radiogoniometry system is to estimate the incidence of a transmitter, i.e. the angles of arrival of radioelectric waves incident on a network 1 of N sensors of a reception system 2, for example a network of several antennas as represented in FIGS. 1 and 2. The network of N sensors is coupled to a computation device 4 via N receivers in order to estimate the angles of incidence xcex8p of the radioelectric waves transmitted by various sources p or transmitters and which are received by the network.
The wave transmitted by the transmitter can propagate along several paths according to a diagram given in FIG. 3. The wave k(xcex8d) has a direct path with angle of incidence xcex8d and the wave k(xcex8r) a reflected path with angle of incidence xcex8r. The multipaths are due in particular to obstacles 5 located between the transmitter 6 and the reception system 7. At the reception station, the various paths arrive with various angles of incidence xcex8op where p corresponds to the pth path. The multipaths follow different propagation routes and are therefore received at different times tmp.
The N antennas of the reception system receive the signal xn(t) where n is the index of the sensor. Using these N signals xn(t), the observation vector is built:                                           x            _                    ⁡                      (            t            )                          =                  [                                                                                          x                    1                                    ⁡                                      (                    t                    )                                                                                                      .                                                                    .                                                                                                          x                    n                                    ⁡                                      (                    t                    )                                                                                ]                                    (        1        )            
With M transmitters this observation vector x(t) is written as follows:                                           x            _                    ⁡                      (            t            )                          =                                            ∑                              m                =                1                            M                        ⁢                                          ∑                                  p                  =                  1                                                  P                  m                                            ⁢                                                ρ                  mp                                ⁢                                                      a                    _                                    ⁡                                      (                                          θ                      mp                                        )                                                  ⁢                                                      s                    m                                    ⁡                                      (                                          t                      -                                              τ                        mp                                                              )                                                                                +                                    b              _                        ⁡                          (              t              )                                                          (        2        )            
where
a(xcex8mp) is the steering vector of the pth path of the mth transmitter. The vector a(xcex8) is the response of the network of N sensors to a source of incidence xcex8
xcfx81mp is the attenuation factor of the pth path of the mth transmitter
xcfx84mp is the delay of the pth path of the mth transmitter
Pm is the number of multipaths of the mth transmitter
sm(t) is the signal transmitted by the mth transmitter
b(t) is the noise vector composed of the additive noise bn(t) (1xe2x89xa6nxe2x89xa6N) on each sensor.
The prior art describes various techniques of goniometry, of source separation and of goniometry after the separation of the source.
These techniques consist of estimating the signals sm(txe2x88x92xcfx84mp) from the observation vector x(t) with no knowledge of their time properties. These techniques are known as blind techniques. The only assumption is that the signals sm(txe2x88x92xcfx84mp) are statistically independent for a path p such that 1xe2x89xa6pxe2x89xa6Pm and for a transmitter m such that 1xe2x89xa6mxe2x89xa6M. Knowing that the correlation between the signals sm(t) and sm(txe2x88x92xcfx84) is equal to order 2 to the autocorrelation function rsm(xcfx84)=E[sm(t)sm(txe2x88x92xcfx84)*] of the signal sm(t), we deduce that the multipaths of a given signal sm(t) transmitter are dependent since the function rsm(xcfx84) is non null. However, two different transmitters m and mxe2x80x2, of respective signals sm(t) and smxe2x80x2(t), are statistically independent if the relation E[sm(t) smxe2x80x2(t)*]=0 is satisfied, where E[.] is the expected value. Under these conditions, these techniques can be used when the wave propagates in a single path, when P1= . . . =PM=1. The observation vector x(t) is then expressed by:                                           x            _                    ⁡                      (            t            )                          =                                                            ∑                                  m                  =                  1                                M                            ⁢                                                                    a                    _                                    ⁡                                      (                                          θ                      m                                        )                                                  ⁢                                                      s                    m                                    ⁡                                      (                    t                    )                                                                        +                                          b                _                            ⁡                              (                t                )                                              =                                    A              ⁢                              xe2x80x83                            ⁢                                                s                  _                                ⁡                                  (                  t                  )                                                      +                                          b                _                            ⁡                              (                t                )                                                                        (        3        )            
where A=[a(xcex81) . . . a(xcex8M)] is the matrix of steering vectors of the sources and s(t) is the source vector such that s(t)=[s1(t) . . . sM(t)]T (where the exponent T designates the transpose of vector u which satisfies in this case u=s(t)).
These methods consist of building a matrix W of dimension (Nxc3x97M), called separator, generating at each time t a vector y(t) of dimension M which corresponds to a diagonal matrix and, to within one permutation matrix, to an estimate of the source vector s(t) of the envelopes of the M signals of interest to the receiver. This problem of source separation can be summarised by the following expression of the required vectorial output at time t of the linear separator W:
y(t)=WHx(t)=Πxcex9ŝ(t)xe2x80x83xe2x80x83(4) 
where Π and xcex9 correspond respectively to arbitrary permutation and diagonal matrices of dimension M and where ŝ(t) is an estimate of the vector s(t). WH designates the transposition and conjugation operation of the matrix W.
These methods involve the statistics of order 2 and 4 of the observation vector x(t).
Order 2 Statistics: Covariance Matrix
The correlation matrix of the signal x(t) is defined by the following expression:
Rxx=E[x(t)x(t)H]xe2x80x83xe2x80x83(5) 
Knowing that the source vector s(t) is independent of the noise b(t) we deduce from (3) that:
Rxx=ARssAH+"sgr"2Ixe2x80x83xe2x80x83(6) 
Where Rss=E[s(t) s(t)H] and E[b(t) b(t)H]="sgr"2I.
The estimate of Rxx used is such that:                                           R            ^                    xx                =                              1            T                    ⁢                                    ∑                              t                =                1                            T                        ⁢                                                            x                  _                                ⁡                                  (                  t                  )                                            ⁢                                                                    x                    _                                    ⁡                                      (                    t                    )                                                  H                                                                        (        7        )            
where T corresponds to the integration period.
Order 4 Statistics: Quadricovariance
By extension of the correlation matrix, we define with order 4 the quadricovariance whose elements are the cumulants of the sensor signals xn(t):
Qxx(i,j,k,l)=cum{xi(t), xj(t)*, xk(t)*, xl(t)}xe2x80x83xe2x80x83(8)                                                                         With                ⁢                                  xe2x80x83                                ⁢                cum                ⁢                                  {                                                            y                      i                                        ,                                          y                      j                                        ,                                          y                      k                                        ,                                          y                      i                                                        }                                            =                                                E                  ⁡                                      [                                                                  y                        i                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        j                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        k                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        l                                                              ]                                                  -                                  xe2x80x83                                ⁢                                                      E                    ⁡                                          [                                                                        y                          i                                                ⁢                                                  xe2x80x83                                                ⁢                                                  y                          j                                                                    ]                                                        ⁡                                      [                                                                  y                        k                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        l                                                              ]                                                                                                                          -                              xe2x80x83                            ⁢                                                E                  ⁡                                      [                                                                  y                        i                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        k                                                              ]                                                  ⁡                                  [                                                            y                      j                                        ⁢                                          xe2x80x83                                        ⁢                                          y                      l                                                        ]                                                                                                        -                              xe2x80x83                            ⁢                                                E                  ⁡                                      [                                                                  y                        i                                            ⁢                                              xe2x80x83                                            ⁢                                              y                        l                                                              ]                                                  ⁡                                  [                                                            y                      j                                        ⁢                                          xe2x80x83                                        ⁢                                          y                      k                                                        ]                                                                                        (        9        )            
Knowing that N is the number of sensors, the elements Qxx(i,j,k,l) are stored in a matrix Qxx at line number N(jxe2x88x921)+i and column number N(lxe2x88x921)+k. Qxx is therefore a matrix of dimension N2xc3x97N2.
It is also possible to write the quadricovariance of observations x(t) using the quadricovariances of the sources and the noise written respectively Qss and Qbb. Thus according to expression (3) we obtain:                               Q          xx                =                                            ∑                              i                ,                j                ,                k                ,                l                                      ⁢                                                                                                      Q                      ss                                        ⁡                                          (                                              i                        ,                        j                        ,                        k                        ,                        l                                            )                                                        ⁡                                      [                                                                                            a                          _                                                ⁡                                                  (                                                      θ                            i                                                    )                                                                    ⊗                                                                                                    a                            _                                                    ⁡                                                      (                                                          θ                              j                                                        )                                                                          *                                                              ]                                                  ⁡                                  [                                                                                    a                        _                                            ⁡                                              (                                                  θ                          k                                                )                                                              ⊗                                                                                            a                          _                                                ⁡                                                  (                                                      θ                            l                                                    )                                                                    *                                                        ]                                            H                                +                      Q            bb                                              (        10        )            
where {circle around (x)} designates the Kronecker product such that:                                           u            _                    ⊗                      v            _                          =                                            [                                                                                                                  u                        _                                            ⁢                                              xe2x80x83                                            ⁢                                              v                        1                                                                                                                                  .                                                                                                                                      u                        _                                            ⁢                                              xe2x80x83                                            ⁢                                              v                        K                                                                                                        ]                        ⁢                          xe2x80x83                        ⁢            where            ⁢                          xe2x80x83                        ⁢                          v              _                                =                      [                                                                                v                    1                                                                                                .                                                                                                  v                    K                                                                        ]                                              (        11        )            
Note that when there are independent sources, the following equality (12) is obtained:       Q    xx    =                    ∑                  m          =          1                M            ⁢                                                                  Q                ss                            ⁢                              (                                  m                  ,                  m                  ,                  m                  ,                  m                                )                                      ⁢                          xe2x80x83                        [                                          a                _                            ⁢                                                (                                      θ                    m                                    )                                ⊗                                                                            a                      _                                        ⁡                                          (                                              θ                        m                                            )                                                        *                                                      ]                    ⁢                      xe2x80x83                    [                                    a              _                        ⁢                                          (                                  θ                  m                                )                            ⊗                                                                    a                    _                                    ⁡                                      (                                          θ                      m                                        )                                                  *                                              ]                H              +          Q      bb      
Since Qss(i,j,k,l)=0 for ixe2x89xa0jxe2x89xa0kxe2x89xa0l. In addition, in the presence of Gaussian noise the quadricovariance Qbb of the noise cancels out and leads to (13):       Q    xx    =            ∑              m        =        1            M        ⁢                                                      Q              ss                        ⁢                          (                              m                ,                m                ,                m                ,                m                            )                                ⁢                      xe2x80x83                    [                                    a              _                        ⁢                                          (                                  θ                  m                                )                            ⊗                                                                    a                    _                                    ⁡                                      (                                          θ                      m                                        )                                                  *                                              ]                ⁢                  xe2x80x83                [                              a            _                    ⁢                                    (                              θ                m                            )                        ⊗                                                            a                  _                                ⁡                                  (                                      θ                    m                                    )                                            *                                      ]            H      
An example of a known source separation method is the Souloumiac-Cardoso method which is described, for example, in document [1] entitled xe2x80x9cBlind Beamforming for Non Gaussian Signalsxe2x80x9d, authors J. F. CARDOSO, A. SOULOUMIAC, published in the review IEE Proc-F, Vol 140, No. 6, pp 362-370, December 1993.
FIG. 4 schematises the principle of this separation method based on the statistical independence of sources. Under these conditions, the matrices Rss and Qss of expressions (6) and (10) are diagonal. This figure shows that the algorithm used to process the observation vector corresponding to the signals received on the sensor network is composed of a data x(t) whitening step 10 resulting in an observation vector z(t), and a steering vector identification step 11, possibly followed by a spatial filtering step 12 using the signal vector x(t) to obtain an estimated signal ŝxe2x80x2(t). The whitening step uses the covariance matrix Rxx in order to orthonormalise the basis of the steering vectors a(xcex81) . . . a(xcex8M). The second identification step uses the quadricovariance Qzz to identify the steering vectors previously orthonormalised.
The coefficients of the spatial filtering step Wi are defined as follows
wi=aRxxe2x88x921a(xcex8i) 
Whitening Step
Whitening is carried out to orthogonalise the mixture matrix A to be estimated. The observations x(t) must be multiplied by a matrix "THgr"xe2x88x921 such that the covariance matrix of denoised and whitened observations is equal to the identity matrix. z(t) represents the vector of noised and whitened observations:
z(t)="THgr"xe2x88x921x(t)="THgr"xe2x88x921As(t)+"THgr"xe2x88x921b(t)xe2x80x83xe2x80x83(14) 
The matrix "THgr" of dimension Nxc3x97M must then satisfy according to (6) the following relation:
"THgr""THgr"H=Rxxxe2x88x92Rbb=ARssAHxe2x80x83xe2x80x83(15) 
Knowing that E[b(t) b(t)H]="sgr"2 I, we deduce from (6) that the decomposition into eigenelements of Rxx satisfies:
Rxx=Esxcex9sEsH+"sgr"2EbEbHxe2x80x83xe2x80x83(16) 
Where xcex9s is a diagonal matrix of dimension Mxc3x97M containing the M largest eigenvalues of Rxx. The matrix Es of dimension Nxc3x97M is composed of eigenvectors associated with the largest eigenvalues of Rxx and the matrix Eb of dimension Nxc3x97(Nxe2x88x92M) is composed of eigenvectors associated with the noise eigenvalue "sgr"2. Knowing firstly that Rbb=E[b(t) b(t)H]="sgr"2 I and that secondly by definition from the decomposition into eigenelements that (Es EsH+Eb EbH)=I, we deduce from (15) that:
"THgr""THgr"H=A RssAH=Es(xcex9sxe2x88x92"sgr"2IM)EsHxe2x80x83xe2x80x83(17) 
We can then take for matrix "THgr" the following matrix of dimension Nxc3x97M.
"THgr"=Es(xcex9sxe2x88x92"sgr"2IM)xc2xdxe2x80x83xe2x80x83(18) 
According to (17) we deduce that the matrix "THgr" also equals:
"THgr"=A Rssxc2xdUH with UHU=IMxe2x80x83xe2x80x83(19) 
U is then a unit matrix whose columns are formed from orthonormed vectors. According to (3), (14) and (19) the vector z(t) of dimension Mxc3x971 can be expressed as follows:
z(t)=Usxe2x80x2(t)+"THgr"xe2x88x921b(t) with sxe2x80x2(t)=Rssxe2x88x92xc2xds(t)xe2x80x83xe2x80x83(20) 
With decorrelated sources, the matrices Rss and Rssxe2x88x92xc2xd are diagonal and so the components of vectors sxe2x80x2(t) and s(t) are equal to within one amplitude such that:                     s        _            xe2x80x2        ⁡          (      t      )        =                    [                                                                                                  s                    1                                    ⁡                                      (                    t                    )                                                  /                                                      γ                    1                                                                                                          .                                                                                                                s                    M                                    ⁡                                      (                    t                    )                                                  /                                                      γ                    M                                                                                      ]            ⁢              xe2x80x83            ⁢      where      ⁢              xe2x80x83            ⁢                        s          _                ⁡                  (          t          )                      =                            [                                                                                          s                    1                                    ⁡                                      (                    t                    )                                                                                                      .                                                                                                          s                    M                                    ⁡                                      (                    t                    )                                                                                ]                ⁢                  xe2x80x83                ⁢        and        ⁢                  xe2x80x83                ⁢                  R          ss                    =              [                                                            γ                1                                                    .                                      0                                                          .                                      .                                      .                                                          0                                      .                                                      γ                M                                                    ]            
The matrix U is composed of whitened steering vectors such that:
U=[tl . . . tM]xe2x80x83xe2x80x83(21) 
Identification Step
The purpose of this step is to identify the unit matrix U composed of M whitened steering vectors tm. According to (20) and (21), the vector z(t) of whitened observations can be expressed as follows:                                                         z              _                        ⁡                          (              t              )                                =                                                    U                ⁢                                  xe2x80x83                                ⁢                                                                            s                      _                                        xe2x80x2                                    ⁡                                      (                    t                    )                                                              +                                                Θ                                      -                    1                                                  ⁢                                                      b                    _                                    ⁡                                      (                    t                    )                                                                        =                                                            ∑                                      m                    =                    1                                    M                                ⁢                                                                            t                      _                                        M                                    ⁢                                                            s                      m                      xe2x80x2                                        ⁡                                          (                      t                      )                                                                                  +                                                                    b                    _                                    xe2x80x2                                ⁡                                  (                  t                  )                                                                    ⁢                  
                ⁢                              with                    ⁢                      xe2x80x83                    ⁢                                    s              m              xe2x80x2                        ⁡                          (              t              )                                      =                                                                              s                  m                                ⁡                                  (                  t                  )                                            /                                                γ                  m                                                      ⁢                          xe2x80x83                        ⁢                          and                        ⁢                          xe2x80x83                        ⁢                                                            b                  _                                xe2x80x2                            ⁡                              (                t                )                                              =                                    Θ                              -                1                                      ⁢                                                            b                  _                                ⁡                                  (                  t                  )                                            .                                                          (        22        )            
Knowing that the M signal sources sxe2x80x2m(t) are independent, we deduce according to (13) that the quadricovariance of z(t) can be written as follows:                               Q          zz                =                              ∑                          m              =              1                        M                    ⁢                                                                                          Q                                                                  s                        xe2x80x2                                            ⁢                                              s                        xe2x80x2                                                                              ⁡                                      (                                          m                      ,                      m                      ,                      m                      ,                      m                                        )                                                  ⁡                                  [                                                                                    t                        _                                            m                                        ⊗                                                                  t                        _                                            m                      *                                                        ]                                            ⁡                              [                                                                            t                      _                                        m                                    ⊗                                                            t                      _                                        m                    *                                                  ]                                      H                                              (        23        )            
Under these conditions, the matrix Qzz of dimension M2xc3x97M2 has rank M. Diagonalisation of Qzz then enables us to retrieve the eigenvectors associated with the M largest eigenvalues. These eigenvectors can be written as follows:                                           e            _                    m                =                                            ∑                              i                =                1                            M                        ⁢                                                            α                  mi                                ⁡                                  (                                                                                    t                        _                                            i                                        ⊗                                                                  t                        _                                            i                      *                                                        )                                            ⁢                              xe2x80x83                            ⁢                              for                            ⁢                              xe2x80x83                            ⁢              m                                =                      1            ⁢                          xe2x80x83                        ⁢            ⋯            ⁢                          xe2x80x83                        ⁢            M                                              (        24        )            
We then transform each vector em of length M2 into a matrix Um of dimension (Mxc3x97M) whose columns are the M M-uplets forming, the vector em.                                           U            m                    =                      (                                                                                e                                          m                      ,                      1                                                                                                            e                                          m                      ,                                              M                        +                        1                                                                                                              ⋯                                                                      e                                          m                      ,                                                                                                    (                                                          M                              -                              1                                                        )                                                    ⁢                          M                                                +                        1                                                                                                                                          ⋮                                                  ⋮                                                  ⋮                                                  ⋮                                                                                                  e                                          m                      ,                      M                                                                                                            e                                          m                      ,                                              2                        ⁢                        M                                                                                                              ⋯                                                                      e                                          m                      ,                                              M                        2                                                                                                                  )                          ⁢                  
                ⁢                                            with                        ⁢                          xe2x80x83                        ⁢                                          e                _                            m                                =                      (                                                                                e                                          m                      ,                      1                                                                                                                    ⋮                                                                                                  e                                          m                      ,                      M                                                                                                                    ⋮                                                                                                  e                                          m                      ,                                                                                                    (                                                          M                              -                              1                                                        )                                                    ⁢                          M                                                +                        1                                                                                                                                          ⋮                                                                                                  e                                                                  m                        .                                            ,                                              M                        2                                                                                                                  )                                              (        25        )            
which according to equation (24) can also be written:                               U          m                =                                            ∑                              i                =                1                            M                        ⁢                                          α                mi                            ⁢                                                t                  _                                i                            ⁢                                                t                  _                                i                H                                              =                      U            ⁢                          xe2x80x83                        ⁢                          δ              m                        ⁢                          U              H                                                          (        26        )            
where xcex4m is a diagonal matrix of elements xcex1mi. To identify the matrix U, simply diagonalise the eigenmatrices Um for 1xe2x89xa6mxe2x89xa6M since the matrix U is a unit matrix due to the whitening step. Reference [1] proposes an algorithm for joint diagonalisation of the M matrices Um.
Knowing the matrices U and "THgr" we can deduce according to (19) the matrix A of steering vectors such that:
"THgr"U=A Rssxc2xd=[axe2x80x2l . . . axe2x80x2M] with axe2x80x2m=a(xcex8m)xc3x97{square root over (xcex3m)}xe2x80x83xe2x80x83(27) 
We therefore identify the steering vectors a(xcex8m) of the sources to within a multiplying factor {square root over (xcex3m)}. According to expressions (20) and (14) and knowing the matrices U and "THgr" we deduce the estimate of the source vector sxe2x80x2(t) such that:                                           s            ^                    _                xe2x80x2            ⁡              (        t        )              =                  U        H            ⁢              Θ                  -          1                    ⁢                        x          _                ⁡                  (          t          )                                        where            ⁢              xe2x80x83            ⁢                                                  s              ^                        _                    xe2x80x2                ⁡                  (          t          )                      =          [                                                                                                        s                    ^                                    1                                ⁡                                  (                  t                  )                                            /                                                γ                  1                                                                                          ⋮                                                                                                                    s                    ^                                    M                                ⁡                                  (                  t                  )                                            /                                                γ                  M                                                                        ]      
knowing that                               R          ss                =                  [                                                                      γ                  1                                                            ⋯                                            0                                                                    ⋮                                            ⋮                                            ⋮                                                                    0                                            ⋯                                                              γ                  M                                                              ]                                    (        28        )            
We therefore estimate the signals sm(t) to within a multiplying factor of value (1/{square root over (xcex3m)}) such that: 
ŝxe2x80x2m(t)=(1/{square root over (xcex3m)}) ŝm(t)xe2x80x83xe2x80x83(29) 
Behaviour with Multipaths
Knowing that, for a given transmitter m, the signals sm(t) and sm(txe2x88x92xcfx84) are correlated, it is possible to deduce the existence of dependence between the signal multipaths sm(txe2x88x92xcfx84mp) with 1 less than p less than Pm.
It was demonstrated in reference [2], authors P. CHEVALIER, V. CAPDEVIELLE, P. COMON, entitled xe2x80x9cBehaviour of HO blind source separation methods in the presence of cyclostationary correlated multipathsxe2x80x9d, published in the IEEE review SP Workshop on HOS, Alberta (Canada), July 1997, that the source separation method separates the transmitters without separating their multipaths. So by taking the signal model of expression (2) for the mth transmitter we identify the following Pm vectors:                                           u            _                    mp                =                                            ∑                              i                =                1                                            P                m                                      ⁢                                          β                mpi                            ⁢                                                a                  _                                ⁡                                  (                                      θ                    mi                                    )                                            ⁢                              xe2x80x83                            ⁢                              for                            ⁢                              xe2x80x83                            ⁢              1                                ≤          p          ≤                      P            m                                              (        30        )            
Similarly for the mth transmitter we identify the following Pm signals:                                                         s              ^                        mp            xe2x80x2                    ⁡                      (            t            )                          =                                            ∑                              i                =                1                                            P                m                                      ⁢                                          β                mpi                xe2x80x2                            ⁢                                                                    s                    ^                                    m                                ⁡                                  (                                      t                    -                                          τ                      mi                                                        )                                            ⁢                              xe2x80x83                            ⁢                              for                            ⁢                              xe2x80x83                            ⁢              1                                ≤          p          ≤                      P            m                                              (        31        )            
These source separation techniques assume, in order to be efficient, that the signals propagate in a single path. The signals transmitted by each transmitter are considered as statistically independent.
With a single path where P1= . . . =Pm=1, the sources are all independent and the M vectors identified at separation output have, according to the relation (27), the following structure:
axe2x80x2m=xcex2ma(xcex8m) for 1xe2x89xa6mxe2x89xa6Mxe2x80x83xe2x80x83(32) 
For each transmitter, the following noise projector Πbm is built:                               ∏          bm                ⁢                  =                                                    I                N                            -                                                                                                                  a                        _                                            m                      xe2x80x2                                        ⁢                                                                  a                        _                                            m                                              xe2x80x2                        ⁢                                                  xe2x80x83                                                ⁢                        H                                                                                                                                                a                        _                                            m                                              xe2x80x2                        ⁢                                                  xe2x80x83                                                ⁢                        H                                                              ⁢                                                                  a                        _                                            m                      xe2x80x2                                                                      ⁢                                  xe2x80x83                                ⁢                                  for                                ⁢                                  xe2x80x83                                ⁢                1                                      ≤            m            ≤            M                                              (        33        )            
By applying the MUSIC principle we then look for the incidence {circumflex over (xcex8)}m of the mth transmitter which cancels the following criterion:                                           θ            ^                    m                =                                                                              min                                                                              θ                                                      ⁢                          {                                                                                          a                      _                                        ⁡                                          (                      θ                      )                                                        H                                ⁢                                                      ∏                    bm                                    ⁢                                                            a                      _                                        ⁡                                          (                      θ                      )                                                                                  }                        ⁢                          xe2x80x83                        ⁢                          for                        ⁢                          xe2x80x83                        ⁢            1                    ≤          m          ≤          M                                    (        34        )            
The principle of the MUSIC algorithm is for example described in document [3] by R. O. Schmidt entitled xe2x80x9cA signal subspace approach to multiple emitters location and spectral estimationxe2x80x9d, PhD Thesis, Stanford University, CA, November 1981.
Thus, using vectors axe2x80x21 . . . axe2x80x2M identified at source separation output it is possible to deduce the incidences {circumflex over (xcex8)}1 . . . {circumflex over (xcex8)}M for each transmitter. However, the sources must be decorrelated if the vectors identified are to satisfy the relation axe2x80x2m=xcex2m a (xcex8m).
For example, in document [4] entitled xe2x80x9cDirection finding after blind identification of sources steering vectors: The Blind-Maxcor and Blind-MUSIC methodsxe2x80x9d, authors P. CHEVALIER, G. BENOIT, A. FERREOL, and published in the review Proc. EUSIPCO, Triestre, September 1996, a blind-MUSIC algorithm of the same family as the MUSIC algorithm, known by those skilled in the art, is applied.
The known techniques of the prior art can therefore be used to determine the incidences for the various transmitters if the wave transmitted for each of these transmitters propagates as monopath.
The invention concerns a method and a device which can be used to determine in particular, for each transmitter propagating as multipaths, the incidences of the arrival angles for the multipaths.
The purpose of this invention is to carry out selective goniometry by transmitter in the presence of multipaths, i.e. for Pm greater than 1.
One of the methods implemented by the invention is to group the signals received for each transmitter, before carrying out the goniometry of all these multipaths for each transmitter, for example.
Another method consists of space-time separation of the sources or transmitters.
In this description, the following terms are defined:
Ambiguities: we have an ambiguity when the goniometry algorithm can estimate with equal probability either the true incidence of the source or another quite different incidence. The greater the number of sources to be identified simultaneously, the greater the risk of ambiguity.
Multipath: when the wave transmitted by a transmitter propagates along several paths towards the goniometry system. Multipaths are due to the presence of obstacles between a transmitter and a receiver.
Blind: with no a priori knowledge of the transmitting sources.
The invention concerns a method for space-time estimation of the angles of incidence of one or more transmitters in an antenna network wherein it comprises at least a step to separate the transmitters and a step to determine the various arrival angles xcex8mi of the multipaths p transmitted by each transmitter.
According to a first mode of realisation, the method comprises at least a step to separate the transmitters in order to obtain the various signals s(t) received by the antenna network, a step to group the various signals by transmitter and a step to determine the various angles xcex8mi of the multipaths by transmitter.
The step to group the various signals by transmitter comprises for example:
a step to intercorrelate two by two the components uk(t) of the signal vector sxe2x80x2(t) resulting from the source separation step,
a step to find the delay value(s) in order to obtain a maximum value for the intercorrelation function, rkkxe2x80x2(xcfx84)=E[uk(t)ukxe2x80x2(txe2x88x92xcfx84)*],
a step to store the various path indices for which the correlation function is a maximum.
The method comprises for example a step to determine delay times using the incidences xcex8mi, the signal sm(t) and the search for the maximum of the criterion Crii(xcex4xcfx84) to obtain xcex4xcfx84mi=xcfx84mixe2x88x92xcfx84ml, with Crii(xcex4xcfx84)=E[sm(t)(i)sm(txe2x88x92xcex4xcfx84)(1)*].
According to a second realisation variant, the method comprises a step of space-time separation of the various transmitters before determining the various arrival angles xcex8mi.
The space-time separation step comprises for example a step where, for a given transmitter, the signal sm(t) is delayed, thereby comparing the delayed signal to the output of a filter of length Lm, whose inputs are sm(t) up to sm(txe2x88x92xcfx84m), before applying the source separation.
The method may comprise a step to identify and eliminate the outputs associated with the same transmitter after having determined the angles xcex8mi.
The method implements, for example, different types of goniometry, such as high resolution methods such as in particular MUSIC, interferometry methods, etc.
The method applies to the goniometry of multipath sources and also when P1= . . . =Pm=1.
The invention also concerns a device to make a space-time estimation of a set of transmitters which transmit waves propagating as multipaths in a network of N sensors wherein it comprises a computer designed to implement the steps of the method characterised by the steps described above.
The method according to the invention can be used in particular to carry out separate goniometry of the transmitters. Thus, only the incidences of the multipaths of a given transmitter are determined.
Under these conditions, compared with a traditional technique which must simultaneously locate all the transmitters with their multipaths, the method can be used to perform goniometry on fewer sources.